A particle has two energy states having energies $E_0$ and $E_1$ with degeneracies $g_0$ and $g_1$. The respective probabilities are $p_1$ and $p_2$. What is the entropy in terms of $p_1$, $p_2$, $g_1$ and $g_2$ ?

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1 Answer
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In most problems like this, the data $g_1$, $g_2$, $E_0$ and $E_1$ would let you calculate the state occupancy probabilities $p_1$ and $p_2$, through the Boltzmann Distribution. To do this calculation, you would also need the thermodynamic temperature (see the first equations on the Wiki page).

But here $p_1$ and $p_2$ are given to you, as though someone has already done this calculation for you.

The OP does need to know the degeneracies, as there are $g_1$ states with probability $p_1$ and $g_2$ states with probability $p_2$, so the entropy has $g_1 + g_2$ terms.
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NathanielSep 12 '13 at 14:50